What is the definition of economic efficiency?
I. A. What is the definition of economic efficiency? (A one-sentence answer is sufficient for this part of the question.)
B. Briefly explain why being inefficient is considered undesirable. Does this mean that any change that moves the economy from an inefficient situation to an efficient one is desirable? Why or why not?
II. One of the conditions for economic efficiency with respect to any two private goods is that their marginal rate of substitution is equal to their marginal rate of transformation. For example, the condition for wine and bread is MRSWB = MRTWB.
A. Explain why this is a necessary condition for economic efficiency.
B. Explain why perfectly competitive markets would result in this efficiency condition being satisfied.
C. Suppose that the wine industry is perfectly competitive and the bread industry is a monopoly. Explain why the MRSWB = MRTWB condition will not be satisfied. What will be the effect, if any, on the amount of wine relative to the efficient amount?
III. A. What is the definition of dynamic efficiency? (A one-sentence answer is sufficient for this part of the question.)
B. Write down two, equivalent, conditions for dynamic efficiency to be attained.
C. Explain why perfectly competitive capital markets would result in dynamic efficiency being attained.
IV. A. If the real rate of interest is 10%, what is the net present value of a project with net benefits, measured in constant dollars, equal to -$1400.00 in year 0 and $600.00 in each of the next three years? (Show your calculations.)
B. Suppose there is no inflation and an insurance company offers a contract that would pay $500,000 with certainty 50 years from now. What is the most that this contract would be worth today if:
1. The rate of interest is 7%. 2. The rate of interest is 3%.
C. Suppose that you are considering planting some Douglas fir trees this year that will be harvested in 80 years. There is no inflation, the real rate of interest is 10%, and the cost of planting each tree is $4.00. What would each tree be worth at the time of harvest? 1
Forestry economics The table below contains data that are required for some of the following questions. f and ? are derived from a logistic growth function, p = 3, c = 1, .and i = 4.5%.
t 10 11 12 13 14 15 16 17 18 19 20 f ? ?/f f/t (p-c)? i(p-c)f 31.17 35.07 38.46 41.28 43.52 45.25 46.56 47.52 48.23 48.74 49.10 4.11 3.66 3.11 2.52 1.97 1.50 1.12 0.82 0.60 0.43 0.31 13.2% 10.4% 8.1% 6.1% 4.5% 3.3% 2.4% 1.7% 1.2% 0.9% 0.6% 3.12 3.19 3.21 3.18 3.11 3.02 2.91 2.80 2.68 2.57 2.46 8.2 7.3 6.2 5.0 3.9 3.0 2.2 1.6 1.2 0.9 0.6 2.8 3.2 3.5 3.7 3.9 4.1 4.2 4.3 4.3 4.4 4.4
V. Irving Fisher derived a rule for the optimal age of harvesting for the case in which there would be no replanting of the trees.
A. Derive the Fisher rule from the condition MBW = MCW.
B. Applying the Fisher rule to the data in the table, what is the optimal age to harvest the trees? Explain why.
C. What rate of interest would result in maximizing the amount of wood? Explain why.
D. Calculate what the optimal harvesting age would be if each of the following occurred: 1. A trend in the stumpage price equal to ?1.6% per year. 2. A decrease in the interest rate equal to 2.1%.
E. How would a one-time downward shift in the stumpage price affect the optimal harvesting age if the present value of the forest land in an alternative use is A dollars?
VI. Now suppose that the land will be used to grow a new crop of trees when the current crop is harvested, to grow still another crop after the new one is harvested, and so on forever.
A. Explain why the Fisher rule would not be the correct way to determine the optimal harvesting age:
B. Another incorrect rule is the maximum sustainable yield (MSY) rule.
1. What rotation age maximizes MSY? 2. Why wouldn’t it be the correct way to determine the optimal harvesting age?
VII. Now suppose that in addition to growing wood, the forest produces other benefits such as flood control and recreation. Discuss how this would be expected to affect the optimal age for harvesting the trees in each of the following cases:
A. There will be no replanting of the trees.
B. A new crop of trees will be replanted after each harvest, forever. 2 Fishery Economics
VIII. If the equation for sustainable yield is S? = 0.7S(1 – S/100), what is the value of SMSY?
IX. Discuss the following propositions.
A. If the size of the stock of fish does not affect harvesting costs, the optimal stock of fish will be less than or equal to SMSY.
B. If the stock of fish does affect the cost of harvesting, the optimal stock of fish may be greater than SMSY.
X. Suppose that the sustainable harvest function for some type of fish is, H = 5E – 0.15E2, where H is the sustainable harvest measured in pounds of fish and E is the level of fishing effort. The price of fish, P, is $2 per pound, and the expenditure per unit of fishing effort, W, is $2.
A. Write down the equations for total revenue and total expenditure as functions of effort.
B. Solve for the equilibrium levels of effort and harvest that would exist in the absence of any government intervention, assuming that the fishery is an open-access resource.
C. What is the social net benefit from the fishery at these levels of effort and harvest?
D. Derive the equations for marginal revenue and marginal expenditure.
E. Solve for the efficient levels of effort and harvest, E* and H*.
F. What is the social net benefit from the fishery at these levels of effort and harvest?
G. Suppose that technological progress makes it possible to reduce the expenditure per unit of fishing effort from $2 to $0.8. 1. What would be the levels of effort and harvest in the new open-access equilibrium? 2. Compare the results here with the results in B with respect to equilibrium levels of effort and harvest.
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